The first of those is Wednesday's visit to title contenders Manchester City and with games rapidly running out, the Wearsiders must start picking up points sooner rather than later if they want to avoid the drop.
The speculation concerning Poyet's future at Sunderland intensified after he suggested at Tuesday's pre-match news conference that there was "something wrong" at the club a succession of managers had been unable to address.
The Uruguayan, who replaced fiery Italian manager Paolo Di Canio in October, said he became aware of rumours regarding his position when he was contacted by his son.
"He asked 'did you leave?' and I didn't know what he meant," the former Brighton boss told reporters.
"Had I left a restaurant? Had I left home? Why are people expecting me to walk out? I don't know why people have that impression of me.
"If I thought it was time to resign, or I wanted to resign then I would resign, but the situation here has never reached that point. I find myself in a situation I don't like but I'm looking for a solution.
"I'm coming from a place where to resign is natural, because you kind of tell the club 'maybe it's me that's the problem' and people would accept that naturally. But that would be looked at as quitting and I'm not going to quit. Simple. That I can promise you."
Sunderland have picked up just one point from their past eight matches and after a 5-1 defeat to Tottenham Hotspur nine days ago, Poyet said they needed a miracle to avoid dropping into the second-tier Championship.
Despite saying he would not resign, his future could hinge on talks with club owner Ellis Short, where he would put forward his plans for improving the club, who have spent seven consecutive seasons in the Premier League.
"You can describe that meeting as 'make it or break it'," the 46-year-old said.
"But at every club, you have a meeting at the end of the season. You put across your situation and they put across their situation," he added.
"Then you discuss things. That doesn't mean you don't want to be here or you're going against the club. I'm just trying to get the best situation for Sunderland - but also for me.
"If I can get certain things in place and certain standards, then I know I'm going to be able to do my job better. For those standards to be there you need a certain group of players with a certain mentality."
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